The nuisance caused by smoke from a domestic property or non-dark smoke from an industrial or trade premises would be considered a statutory nuisance by the Environmental Health section.
There may also be implications under Waste Management Regulations if the material being burnt is waste and you may also wish to contact Natural Resources Wales - 0300 065 3000 (Mon-Fri, 9am-5pm)
Seven North Wales Authorities, with the assistance of Chartered Institute of Environmental Health have created a dark smoke leaflet which contains the Ringelmann Smoke chart. This can be used to measure the level of dark smoke and is available if you contact the department.
The attached version of the form can be used as a guide, however the colours shown could vary to the original leaflet.